This is possibly not the kind of math application you can share all the details with a class, as its seems a little complicated. In fact, for the NBA to pull this off takes takes several cameras and expensive software.
I first came across some information on how this is done while reading the June 30th issue of Sport Illustrated, "Computers break down the images into voxels (3-D pixels) and the view from any point on the court or field can be re-created into a three-dimensional, 360-degree video of the action."
That didn't tell me a lot, but it did give me the term "voxels" that I could Google.
From WhatIs.com (http://whatis.techtarget.com/definition/voxel) I found this.
"A voxel is a unit of graphic information that defines a point in three-dimensional space. Since a pixel (picture element) defines a point in two dimensional space with its x and y coordinates, a third z coordinate is needed. In 3-D space, each of the coordinates is defined in terms of its position, color, and density. Think of a cube where any point on an outer side is expressed with an x , y coordinate and the third, z coordinate defines a location into the cube from that side, its density, and its color. With this information and 3-D rendering software, a two-dimensional view from various angles of an image can be obtained and viewed at your computer.
Medical practitioners and researchers are now using images defined by voxels and 3-D software to view X-rays, cathode tube scans, and magnetic resonance imaging (MRI) scans from different angles, effectively to see the inside of the body from outside. Geologists can create 3-D views of earth profiles based on sound echoes. Engineers can view complex machinery and material structures to look for weaknesses."
So getting to see NBA replays in 3D is cool, but probably a little trivial. It was interesting to see the application to medicine and geology.
There turned out to be quite a few hits on "voxels". A lot of them dealing with buying the above mentioned software.
Regarding medical applications, the Scientific American website had an interesting article (http://blogs.scientificamerican.com/observations/whats-a-voxel-and-what-can-it-tell-us-a-primer-on-fmri/) on how voxels can be an improvement over regular MRIs.
From another site I found that while "pixel" is short for picture element, "voxel" is short for volume element. That makes sense. Much of the other information I found does not make a lot of sense to me.
From Webopedia.com I found this info: Voxelization is the process of adding depth to an image using a set of cross-sectional images known as a volumetric dataset. These cross-sectional images (or slices) are made up of pixels. The space between any two pixels in one slice is referred to as interpixel distance, which represents a real-world distance.
This article quickly spiraled away from my level of understanding, but this part kind of made sense. For the NBA 3D replay, perhaps each "slice" is the 2D view from a particular camera. Combining this with several other cameras gives various slices. The distances between those slices constitute the third dimension for various points. I don't know, but I might be onto something. Next week will be a new topic, or possibly, if I gain any big insights into voxels, maybe Part 2 of this topic.
